Receiver operating characteristic curves

Researchers evaluated the performance of a cognitive test called “test your memory” as a screening test for Alzheimer’s disease. The screening test is designed to use minimal operator time and to be suitable for non-specialist use. It is self administered under medical supervision. The test has a minimum score of zero and a maximum score of 50; lower scores indicate greater cognitive impairment.1

The study was based in hospital outpatient departments. Participants included 94 patients diagnosed as having Alzheimer’s disease. For each patient, three age matched healthy controls without Alzheimer’s disease (n=282) were recruited from accompanying relatives. All patients and controls completed the screening test.

The optimal test score for discriminating between patients with Alzheimer’s disease and controls was investigated. Each score from 50 down to zero was taken successively as the cut-off point between a “negative” and “positive” screening test result; all scores less than or equal to the cut-off score were considered positive and others were considered negative. For each cut-off score the sensitivity and specificity of the screening test was calculated, and these values were used to derive a receiver operating characteristic curve (figure⇓). The area under the receiver operating characteristic curve was 0.95.

Which of the following statements, if any, are true?

• a) For successive cut-off scores, as the sensitivity of the screening test decreases in value the …